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    "<a id=\"week0\"></a>\n",
    "<h1 style=\"color:#00A6D6;\">Week 0: Quantum Information 101</h1>\n",
    "\n",
    "Welcome to the lab exercises in Julia. These notebooks are meant to help you study the material by performing many calculations in an easy and intuitive manner - in short, by playing around!\n",
    "\n",
    "Each notebook consists of two parts: First, we will show you how to perform certain calculations in Julia and to visualize them. You may wish to change the examples, or extend them to perform other calculations that help you with the material in our class and beyond. \n",
    "\n",
    "Second, each note book as a few Homework exercises marked \"edX Exercises\". These are calculations that we would definitely like you to perform. The answers of these need to be entered into the edX system as they will be graded as part of the class. Completion of these exercises accounts for 20% of the total course completion.\n",
    "\n",
    "If you have never used a Julia sheet before, you may first want to begin with the \"Getting Started\" notebook. \n",
    "\n",
    "Ready? Then let's get started! Click shift-enter in the box below to load the first snippet of Julia!"
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    "# load functions/globals used throughout the notebook\n",
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    "* <a href=\"#single_qubit\"> The Single Qubit </a>\n",
    "\n",
    "* <a href=\"#two_qubits\"> Two Qubits </a>\n",
    "\n",
    "* <a href=\"#measurements\"> Measurements </a>\n",
    "\n",
    "* <a href=\"#transformations\"> Unitary Transformations </a>\n",
    "\n",
    "* <a href=\"#bloch_sphere\"> Bloch Sphere </a>"
   ]
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   "source": [
    "------\n",
    "<a id=\"single_qubit\"></a>\n",
    "<h2 style=\"color:#00A6D6;\">The Single Qubit</h2>\n",
    "\n",
    "Let's start with a single qubit! As you've learned in the videos - and you may want to recap with the lecture notes - the word qubit refers to a quantum bit. \n",
    "\n",
    "Throughout we will use the bra-ket notation, the quantum information way of writing down vectors. Let's remember what the two vectors corresponding to the two classical bits 0 and 1 look like.\n",
    "\n",
    "$$\\left| 0 \\right\\rangle := \\begin{pmatrix}1 \\\\ 0\\end{pmatrix}, \\quad \\text{and} \\quad \\left| 1 \\right\\rangle := \\begin{pmatrix}0 \\\\ 1\\end{pmatrix}.$$\n",
    "\n",
    "Let's define them in Julia:"
   ]
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    "# The vector corresponding to |0>\n",
    "v0 = [1; 0]"
   ]
  },
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   "cell_type": "code",
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   "source": [
    "# The vector corresponding to |1>\n",
    "v1 = [0; 1]"
   ]
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   "cell_type": "markdown",
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   "source": [
    "Accordingly, we can describe the state $\\left| \\psi \\right\\rangle$ of a qubit in general by\n",
    "\n",
    "$$\\left| \\psi \\right\\rangle = \\alpha \\left| 0 \\right\\rangle + \\beta \\left| 1 \\right\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix} \\:.$$\n",
    "\n",
    "The parameters $\\alpha$ and $\\beta$ are amplitudes. Let's try constructing such a vector for some values of $\\alpha$ and $\\beta$ in Julia:"
   ]
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    "# Amplitudes\n",
    "alpha = 1/sqrt(2); # note, by ending a line with a semi-colon output is supressed\n",
    "beta = 1/sqrt(2);  # try adding a semi-colon to the last line of this cell to see what happens\n",
    "\n",
    "# The qubit psi corresponding to such amplitudes\n",
    "psi = alpha * v0 + beta * v1"
   ]
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   "source": [
    "---\n",
    "\n",
    "<a id='normalization'></a>\n",
    "<h4 style=\"color:#00A6D6;\">Normalization</h4>\n",
    "\n",
    "Remember that for $\\left| \\psi \\right\\rangle$ to be a valid qubit we require $\\left| \\psi \\right\\rangle$ to be normalized. For the inner product of $\\left| \\psi \\right\\rangle$ with itself&mdash;in bra-ket notation as $ \\langle \\psi \\:|\\: \\psi \\rangle$&mdash;it must be that\n",
    "\n",
    "$$ \\langle \\psi \\:|\\: \\psi \\rangle = \\lvert\\alpha\\rvert^2 + \\lvert\\beta\\rvert^2 = 1$$\n",
    "\n",
    "To make this more explicit recall that a bra $\\left\\langle \\psi \\right|$ denotes the complex conjugate of the ket $\\left| \\psi \\right\\rangle$:\n",
    "\n",
    "$$\\left\\langle \\psi \\right|:= \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix}^{*T} = \\begin{pmatrix} \\alpha^* , \\beta^* \\end{pmatrix} \\:.$$ \n",
    "\n",
    "Let's expand this in terms of the vector: \n",
    "\n",
    "$$\\langle \\psi \\:|\\: \\psi \\rangle = \\begin{pmatrix} \\alpha^*\\:, \\beta^* \\end{pmatrix} \\cdot \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix} = \\alpha \\cdot \\alpha^* + \\beta \\cdot \\beta^* = \\lvert\\alpha\\rvert^2 + \\lvert\\beta\\rvert^2 = 1$$\n",
    "\n",
    "Let's check whether the qubit psi we have defined above is normalized!"
   ]
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   "source": [
    "# In Julia, this gives us the bra of a vector. Let's print it\n",
    "psi'"
   ]
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   "source": [
    "# Let's now check normalization!\n",
    "psi' * psi"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Be careful that the bra is the <b>conjugate</b> transpose - and not merely the transpose! To see this, let's construct a complex vector, where \"im\" is the Julia way of writing the complex i."
   ]
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    "# Let's define a complex vector\n",
    "alpha = 1/sqrt(2);\n",
    "beta = im * 1/sqrt(2);\n",
    "\n",
    "# Let's display the vector\n",
    "psi = alpha * v0 + beta * v1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "1x2 Array{Complex{Float64},2}:\n",
       " 0.707107-0.0im  0.0-0.707107im"
      ]
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     "execution_count": 10,
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   "source": [
    "# And let's display it's bra: the complex conjugate\n",
    "psi'"
   ]
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   "cell_type": "markdown",
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   "source": [
    "As an exercise for yourself, go and adapt the Julia code below to test whether $$|\\Psi\\rangle = \\alpha |0\\rangle + \\beta |1\\rangle$$ with $\\alpha = 1/3$ and $\\beta = 2/3$ is normalized! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
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     "ename": "LoadError",
     "evalue": "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[11], in expression starting on line 2",
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   "source": [
    "# First, let's define again the amplitudes\n",
    "alpha = ...;\n",
    "beta = ...;\n",
    "\n",
    "# Construct the vector psi\n",
    "psi = alpha * v0 + beta * v1;\n",
    "\n",
    "# Compute the inner product <psi|psi>\n",
    "psi'*psi"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "<h4 style=\"color:#00A6D6;\">A real valued example</h4>\n",
    "\n",
    "Remember that $\\alpha$ and $\\beta$ are in general complex numbers! Let us however assume here that $\\alpha$ and $\\beta$ have a real value</b>. The normalization condition thus becomes $\\alpha^2 + \\beta^2 = 1$. \n",
    "\n",
    "To visualize such a qubit, let us make the following parametrization \n",
    "\n",
    "$$\\alpha = \\cos\\theta \\quad \\text{and} \\quad \\beta = \\sin\\theta$$\n",
    "\n",
    "and see how the state vector can be represented in a 2D plot.\n",
    "\n",
    "<b> click in the code block below and press shift+enter, it might take a moment before the resulting image is loaded</b>.\n",
    "\n",
    "You will see a slider appear which lets you set $\\theta$. You will see a plot appear of the corresponding state vector \n",
    "\n",
    "$$\\left| \\psi(\\theta) \\right\\rangle = \\alpha \\left| 0 \\right\\rangle + \\beta \\left| 1 \\right\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix} \\:.$$\n",
    "\n",
    "Use the slider and vary $\\theta$, you will see the state vector representation vary accordingly. As an exercise for yourself, go and investigate the angles for the elements $|0\\rangle$ and $|1\\rangle$ of the standard basis, and the vectors defining the Hadmard basis:\n",
    "\n",
    "$$|+\\rangle = \\frac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle).$$\n",
    "\n",
    "$$|-\\rangle = \\frac{1}{\\sqrt{2}}(|0\\rangle - |1\\rangle).$$"
   ]
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000001B911710>)"
      ]
     },
     "execution_count": 12,
     "metadata": {
      "comm_id": "b379e630-5a28-416a-9285-249781e11036",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "single_state_vector_plot() # load the interactive plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have already seen above how to express $|+\\rangle$ and $|-\\rangle$ in terms of the standard Basis $|0\\rangle$, $|1\\rangle$ above. Since the Hadmard basis is also a basis, we should of course also be able to write $|0\\rangle$ and $|1\\rangle$ in terms of $|+\\rangle$ and $|-\\rangle$. \n",
    "\n",
    "Can you guess by looking at the picture above? Go and find the coefficients $\\alpha_0, \\beta_0$ and $\\alpha_1,\\beta_1$ visually:\n",
    "\n",
    "$$|0\\rangle = \\alpha_0 |+\\rangle + \\beta_0 |-\\rangle$$\n",
    "$$|1\\rangle = \\alpha_1 |+\\rangle + \\beta_1 |-\\rangle$$.\n",
    "\n",
    "Verify your answers using the Julia code below!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[13], in expression starting on line 6",
     "output_type": "error",
     "traceback": [
      "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[13], in expression starting on line 6",
      ""
     ]
    }
   ],
   "source": [
    "# Let's first define the plus and minus state\n",
    "plus = 1/sqrt(2) * (v0 + v1);\n",
    "minus = 1/sqrt(2) * (v0 - v1);\n",
    "\n",
    "# Let's first make the v0 vector by combining plus and minus\n",
    "alpha0 = ...;\n",
    "beta0 = ...;\n",
    "newV0 = alpha0 * plus + beta0 * minus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[14], in expression starting on line 2",
     "output_type": "error",
     "traceback": [
      "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[14], in expression starting on line 2",
      ""
     ]
    }
   ],
   "source": [
    "# And then the new one vector\n",
    "alpha1 = ...;\n",
    "beta1 = ...;\n",
    "newV1 = alpha1 * plus + beta1 * minus"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\">edX Exercise 1</h3>\n",
    "\n",
    "We're now ready for the first edX Exercise - the result of which you need to enter into the edX grading forms. Consider $$\\left| b_0 \\right\\rangle = \\sqrt{\\frac{1}{3}} \\left| 0 \\right\\rangle + \\sqrt{\\frac{2}{3}} \\left| 1 \\right\\rangle$$\n",
    "\n",
    "What real-valued vectors are orthogonal to this vector? In other words given $\\left| b_0 \\right\\rangle$ which $\\left| b_1 \\right\\rangle$ satisfy\n",
    "\n",
    "$$ \\left\\langle b_1 | b_0 \\right\\rangle = 0 \\:?$$\n",
    "\n",
    "<b>Your task is to find parameters $\\alpha_1 \\geq 0$ and $\\beta_1$ such that\n",
    "\n",
    "$$\\left| b_1 \\right\\rangle = \\begin{pmatrix} \\alpha_1 \\\\ \\beta_1 \\end{pmatrix}$$\n",
    "\n",
    "is orthogonal to $\\left| b_0 \\right\\rangle$ </b>.\n",
    "\n",
    "Take a guess, use Julia to find the vector for you, or compute it by hand! By clicking in the code box just below you can fill in values for $\\alpha_1$ and $\\beta_1$ and calculate $ \\left\\langle b_1 | b_0 \\right\\rangle$ to see how you are doing.\n",
    "\n",
    "To start you off we have set $\\alpha_1$ and $\\beta_1$ to $\\sqrt{\\frac{1}{2}}$ and $\\sqrt{\\frac{1}{2}}$ respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "You have entered |b_1> = \n",
      "0.7071067811865476 ⋅|0> + 0.7071067811865476 ⋅|1> \n",
      "\n",
      "The inner product is \n",
      "  < b_0 | b_1 > = \n",
      "[0.9855985596534889]\n"
     ]
    }
   ],
   "source": [
    "# First let's define the vector b0. We'll do this directly as a vector now\n",
    "b0 = [sqrt(1/3) ; sqrt(2/3)];\n",
    "\n",
    "# Set the amplitudes for b1. We'll put some funny amplitudes to start with...\n",
    "alpha1 = sqrt(1/2);\n",
    "beta1 = sqrt(1/2);\n",
    "\n",
    "b1 = [alpha1; beta1]\n",
    "###### \n",
    "println(\"You have entered |b_1> = \")\n",
    "println(\"$alpha1 ⋅|0> + $beta1 ⋅|1> \\n\")\n",
    "println(\"The inner product is \\n  < b_0 | b_1 > = \")\n",
    "println(b0'*b1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\">edX Exercise 2</h3>\n",
    "\n",
    "<b> Calculate the inner product of $$|+\\rangle$$ and $$|0_y\\rangle = \\frac{1}{\\sqrt{2}}(|0\\rangle + i |1\\rangle)\\:.$$ </b>\n",
    "\n",
    "In other words, calculate \n",
    "\n",
    "$$ \\langle 0_y | + \\rangle$$\n",
    "\n",
    "<b> Note: $|0_y\\rangle$ is complex valued. </b>\n",
    "\n",
    "You can enter the $|+\\rangle$ and $|0_y\\rangle$ state numerically in terms of coefficients $\\alpha_1$, $\\beta_1$ and $\\alpha_2$, $\\beta_2$.\n",
    "\n",
    "As is shown, in Julia, complex numbers $z = x + i \\cdot y$ are entered as \n",
    "<pre>\n",
    "z = x + im*y\n",
    "</pre> \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: UndefVarError: .. not defined\nwhile loading In[16], in expression starting on line 6",
     "output_type": "error",
     "traceback": [
      "LoadError: UndefVarError: .. not defined\nwhile loading In[16], in expression starting on line 6",
      ""
     ]
    }
   ],
   "source": [
    "# |+> state\n",
    "# replace the dots \"..\" with the appropriate coefficient\n",
    "# we have filled in a value for α_1\n",
    "# to show you how to fill in the square root of a fraction.\n",
    "α_1 = sqrt(1/2) \n",
    "β_1 = ..\n",
    "\n",
    "plus = [α_1; β_1];\n",
    "\n",
    "# |0>_y state\n",
    "# replace the dots \"..\" with the appropriate coefficient\n",
    "α_2 = .. \n",
    "β_2 = im*sqrt(1/2)\n",
    "\n",
    "y0 = [α_2; β_2];\n",
    "\n",
    "# Compute the inner prduct - your code goes below!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------\n",
    "<a id=\"two_qubits\"></a>\n",
    "<h2 style=\"color:#00A6D6;\">Two Qubits</h2>\n",
    "\n",
    "Of course we will generally have more than one qubit! Remember that the rule for combining the state of two distinct qubits, into a two qubit state. Let $$\\lvert \\psi_i \\rangle = \\alpha_i \\left| 0 \\right\\rangle + \\beta_i \\left| i \\right\\rangle = \\begin{pmatrix} \\alpha_i \\\\ \\beta_i \\end{pmatrix} $$\n",
    "\n",
    "describe the state of the $i$-th qubit. \n",
    "\n",
    "We can describe the state of two qubits by taking the tensor product\n",
    "\n",
    "$$\\left| \\psi_1 \\right\\rangle \\otimes \\left| \\psi_2 \\right\\rangle = \\Big(\\alpha_1 \\left| 0 \\right\\rangle + \\beta_1 \\left| 1 \\right\\rangle \\Big) \\otimes \\Big(\\alpha_2 \\left| 0 \\right\\rangle + \\beta_2 \\left| 1 \\right\\rangle \\Big) =$$\n",
    "\n",
    "$$\\begin{pmatrix} \\alpha_1 \\\\ \\beta_1 \\end{pmatrix} \\otimes \\begin{pmatrix} \\alpha_2 \\\\ \\beta_2 \\end{pmatrix} = \\begin{pmatrix} \\alpha_1 \\begin{pmatrix} \\alpha_2 \\\\ \\beta_2 \\end{pmatrix}  \\\\ \\beta_2 \\begin{pmatrix} \\alpha_2 \\\\ \\beta_2 \\end{pmatrix}  \\end{pmatrix} = \\begin{pmatrix} \\alpha_1 \\cdot \\alpha_2 \\\\ \\alpha_1 \\cdot \\beta_2  \\\\  \\beta_1 \\cdot \\alpha_2 \\\\ \\beta_1 \\cdot \\beta_2 \\end{pmatrix}  $$\n",
    "\n",
    "To illustrate this, let us calculate how the vector associated with $ \\left| \\psi_1 \\right\\rangle \\otimes \\left| \\psi_2 \\right\\rangle$ given $\\left| \\psi_1 \\right\\rangle$ and $\\left| \\psi_2 \\right\\rangle$\n",
    "\n",
    "<b> click in the code block below and press shift+enter to see the results</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Int64,1}:\n",
       " 0\n",
       " 1\n",
       " 0\n",
       " 0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's first define the vectors, adapt the amplitudes to play around!\n",
    "\n",
    "# Define Psi1\n",
    "alpha1 = 1;\n",
    "beta1 = 0;\n",
    "psi1 = [alpha1; beta1];\n",
    "\n",
    "# Define Psi2\n",
    "alpha2 = 0;\n",
    "beta2 = 1;\n",
    "psi2 = [alpha2; beta2];\n",
    "\n",
    "# Compute the tensor product\n",
    "psiTwo = kron(psi1,psi2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\">edX Exercise 3</h3>\n",
    "\n",
    "Consider the following tensor product\n",
    "\n",
    "$$ |0_y\\rangle \\otimes | + \\rangle = \\begin{pmatrix} c_1 \\\\ c_2 \\\\ c_3 \\\\ c_4 \\end{pmatrix} $$\n",
    "\n",
    "<b> Calculate the coefficients $c_1$, $c_2$, $c_3$, $c_4$</b>. \n",
    "\n",
    "Note, $|0\\rangle_y$ has been defined in exercise 2.\n",
    "\n",
    "Similar to the previous exercise you can check if your calculations went well using the code block just below :\n",
    "\n",
    "You can enter the $|0_y\\rangle$ and $|+\\rangle$ state numerically in terms of coefficients $\\alpha_1$, $\\beta_1$ and $\\alpha_2$, $\\beta_2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c_1, c_2, c_3, c_4 approx = 0.5 + 0.0im, 0.5 + 0.0im, 0.0 + 0.5im, 0.0 + 0.5im\n"
     ]
    }
   ],
   "source": [
    "# |0_y> state\n",
    "# replace the dots \"..\" with the appropriate coefficient\n",
    "# we have filled in a value for α_1\n",
    "# to show you how to fill in the square root of a fraction.\n",
    "α_1 = 1/sqrt(2)\n",
    "β_1 = im*sqrt(1/2)\n",
    "\n",
    "y0 = [α_1; β_1];\n",
    "\n",
    "# |0> state\n",
    "# replace the dots \"..\" with the appropriate coefficient\n",
    "α_2 = 1/sqrt(2)\n",
    "β_2 = 1/sqrt(2)\n",
    "z0 = [α_2; β_2];\n",
    "\n",
    "# Compute the tensor product using the kron function\n",
    "ex4_tensor = kron(y0,z0)\n",
    "\n",
    "# Print the output coefficients\n",
    "ex4_tensor_string = join([string(el) for el in round(ex4_tensor,3)],\", \")\n",
    "println(\"c_1, c_2, c_3, c_4 approx = \"*ex4_tensor_string)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----\n",
    "<a id=\"measurements\"></a>\n",
    "<h2 style=\"color:#00A6D6;\">Measurements</h2>\n",
    "\n",
    "Let's now measure some qubits! Chiefly, we will be measuring one - or more - qubits in a basis, where we will write the basis vectors as $|b_j\\rangle$ for outcome \"j\". We saw in the lecture that the probability of obtaining a particular outcome is given by\n",
    "\n",
    "$$P(B=j) := \\lvert \\langle \\psi \\:|\\: b_j \\rangle \\rvert^2 $$\n",
    "\n",
    "<h4 style=\"color:#00A6D6;\">Measuring a real-valued qubit</h4>\n",
    "\n",
    "To gain some intuition, let us now again consider a qubit with real valued amplitudes. Remember, that we can parameterize such a qubit by an angle $\\theta$\n",
    "\n",
    "$$\\left| \\psi(\\theta) \\right\\rangle = \\cos\\theta \\left| 0 \\right\\rangle + \\sin\\theta \\left| 1 \\right\\rangle = \\begin{pmatrix} \\cos\\theta \\\\ \\sin\\theta \\end{pmatrix} \\:.$$\n",
    "\n",
    "Let's now assume the basis that we measure in is also real valued where the outcome j=0 corresponds to the vector \n",
    "\n",
    "$$\\left| b_0 \\right\\rangle = \\begin{pmatrix} \\cos\\gamma \\\\ \\sin\\gamma \\end{pmatrix} \\:.$$\n",
    "\n",
    "Let us visualize $\\lvert \\psi \\rangle$ and $\\lvert b_0 \\rangle$ and calculate the corresponding $p_{b=0}$.\n",
    "\n",
    "<b> Click in the code block below and press shift+enter, it might take a moment before the resulting image is loaded</b>.\n",
    "\n",
    "You will see a sliders appear which lets you set $\\theta$ and $\\gamma$ (in degrees).\n",
    "\n",
    "A plot will appear of the corresponding vectors and $P_{b=0}$ written in the title.\n",
    "\n",
    "Play around with the values of $\\theta$ and $\\gamma$ and see if you can understand what is going."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Slider{Int64}(Signal{Int64}(0, nactions=0),\"θ\",0,-180:15:180,true)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Slider{Int64}(Signal{Int64}(0, nactions=0),\"γ\",0,-180:15:180,true)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000001BEF64E0>)"
      ]
     },
     "execution_count": 19,
     "metadata": {
      "comm_id": "c7fd504e-cbb1-49d6-887f-be87551be5d0",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measurement_plot() # load the interactive plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4 style=\"color:#00A6D6;\">Global phase is irrelevant</h4>\n",
    "\n",
    "Is there a difference between the qubit $|\\psi\\rangle$ and $|\\phi\\rangle = e^{i\\gamma} |\\phi\\rangle$ for some angle $\\gamma \\in \\mathbb{R}$? It turns out that such a global phase $e^{i\\gamma}$ is irrelevant: there is no measurement that will give us any information on such a global phase - or, in other words - a global phase leads to no observable differences as we explain in detail in the lecture notes.\n",
    "\n",
    "Let's try and convince ourselves below by means of some examples, by measuring a qubit, and the one with the global phase in the standard basis. Of course, you may wish to measure in other bases as well!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Complex{Float64},1}:\n",
       " 0.703574+0.0705929im\n",
       " 0.703574+0.0705929im"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Basis to measure in - default is the standard basis\n",
    "b0 = [1; 0];\n",
    "b1 = [0; 1];\n",
    "\n",
    "# State to be measured - default is the plus state\n",
    "psi = [1; 1]/sqrt(2);\n",
    "\n",
    "# Set the global phase\n",
    "gamma = 0.1;\n",
    "phi = e^(im * gamma) * psi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Float64,1}:\n",
       " 0.707107"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the outcome probabilities\n",
    "\n",
    "val = b0'*psi;         # note, we compute the inner produt by multiplying\n",
    "                       # a row vector - here b0' ( the  accent ' transposes b0 ) - \n",
    "                       # and a column vector - here psi.\n",
    "                       # This returns a 1-element array - here val. \n",
    "                       # val[1] returns the first and only entry of this array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Without phase: p0 = 0.5\n",
      "\n",
      "With phase: p0 = 0.5\n",
      "\n"
     ]
    }
   ],
   "source": [
    "p0 = abs(val[1])^2;    \n",
    "\n",
    "val = b0'*phi;\n",
    "p0Phase = abs(val[1])^2;\n",
    "\n",
    "# Round and print\n",
    "digits = 3;\n",
    "p0 = round(p0,digits);\n",
    "p0Phase = round(p0Phase,digits);\n",
    "\n",
    "println(\"Without phase: p0 = \", p0, \"\\n\")\n",
    "println(\"With phase: p0 = \", p0, \"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\"> edX Exercise 4 </h3>\n",
    "\n",
    "Consider the measurement basis \n",
    "\n",
    "$$ \\{ \\left| b_0 \\right\\rangle , \\left| b_1 \\right\\rangle \\} $$\n",
    "\n",
    "with\n",
    "\n",
    "$$ \\left| b_0 \\right\\rangle = \\sqrt{\\frac{1}{3}} \\left| 0 \\right\\rangle + \\sqrt{\\frac{2}{3}} \\left| 1 \\right\\rangle$$\n",
    "\n",
    "and \n",
    "\n",
    "$$\\left| b_1 \\right\\rangle = \\sqrt{\\frac{2}{3}} \\left| 0 \\right\\rangle - \\sqrt{\\frac{1}{3}} \\left| 1 \\right\\rangle$$\n",
    "\n",
    "For different states $ | \\psi \\rangle$ calculate probabilities of obtaining measurement outcomes 0 and 1. That is, compute\n",
    "\n",
    "$$ P(B=0) = p_0 = |\\langle b_0 | \\psi \\rangle|^2 $$\n",
    "\n",
    "and \n",
    "\n",
    "$$ P(B=1) =  p_1 = |\\langle b_1 | \\psi \\rangle|^2 \\:.$$\n",
    "\n",
    "for each of the following states\n",
    "\n",
    "$$ |\\psi_1 \\rangle = |0\\rangle$$\n",
    "\n",
    "$$ |\\psi_2 \\rangle = |+\\rangle$$\n",
    "\n",
    "$$ |\\psi_2 \\rangle = |-\\rangle$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3333333333333334"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This is the basis we will measure in\n",
    "b0 = [1/sqrt(3); sqrt(2/3)];\n",
    "b1 = [sqrt(2/3); 1/sqrt(3)];\n",
    "\n",
    "# Define the states\n",
    "psi1 = [1; 0];\n",
    "psi2 = [0; 0];\n",
    "psi3 = [0; 0];\n",
    "\n",
    "# Write code to compute the probabilities - we'll do it for just one of the cases here.\n",
    "val = b0'*psi1;\n",
    "p0GivenPsi1 = abs(val[1])^2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4 style=\"color:#00A6D6;\"> Supplement to Exercise 4 </h4>\n",
    "\n",
    "It is helpful to visualize the measurement. Run the code below by clicking inside the block of code and pressing shift+enter.\n",
    "\n",
    "You will see a 2D plot of $\\left| b_0 \\right\\rangle$ and $\\left| b_1 \\right\\rangle$ appear. \n",
    "\n",
    "Furthermore a slider labeled $\\theta$ will appear which allows you to select $|\\psi \\rangle = |0\\rangle$, $|\\psi \\rangle = |+\\rangle$ or $|\\psi \\rangle = |-\\rangle$.\n",
    "\n",
    "Accordingly $|\\psi \\rangle$ is plot together with a numerical approximation of \n",
    "\n",
    "$$ p_0 = |\\langle b_0 | \\psi \\rangle|^2$$\n",
    "\n",
    "and \n",
    "\n",
    "$$ p_1 = |\\langle b_1 | \\psi \\rangle|^2 \\:.$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Options{:ToggleButtons,ASCIIString}(Signal{ASCIIString}(0, nactions=0),\"state\",\"0\",\"0\",Interact.OptionDict(Any[\"0\",\"+\",\"-\"],Dict{Any,Any}(\"-\"=>\"-\",\"0\"=>\"0\",\"+\"=>\"+\")),Any[],Any[])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000001C0B6FD0>)"
      ]
     },
     "execution_count": 24,
     "metadata": {
      "comm_id": "ec8c941b-f9d4-409e-b3f8-0161ea771a65",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "projective_measurement_plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\"> Measuring two qubits</h3>\n",
    "\n",
    "Let's now imagine we have two qubits A and B. We will imagine that Alice holds qubits A and Bob holds qubit B. Evidently we might imagine that Alice measures her qubit in a basis... and also Bob could measure his qubit in a basis. What can we say about the overall measurement? \n",
    "\n",
    "Let's consider the example where Alice measures in the in the standard basis\n",
    "\n",
    "$$ |0\\rangle_A = |0\\rangle \\\\ |1\\rangle_A = |1\\rangle$$\n",
    "\n",
    "and Bob measures in the basis; $|0\\rangle_B$, $|1\\rangle_B$; in a \"$\\pi/8$ rotated\" basis\n",
    "\n",
    "$$ |0\\rangle_B = cos \\frac{\\pi}{8} \\cdot |0\\rangle + sin\\frac{\\pi}{8} \\cdot |1\\rangle \\\\ |1\\rangle_B = -sin\\frac{\\pi}{8}|0\\rangle + cos \\frac{\\pi}{8} \\cdot |1\\rangle$$\n",
    "\n",
    "To see how this is a \"$\\pi/8$ rotated\" basis consider the following picture, where we will actually plot the basis of Alice and Bob into the same plot even though they are of course on two different qubits.\n",
    "\n",
    "<b> In case you see no image, click in the code block below and press shift+enter, it might take a moment before the resulting image is loaded</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000001CC01160>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x00000000205D1048>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi8_rotated_basis_plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\">edX Exercise 5 </h3>\n",
    "\n",
    "How can we describe the overall measurement if Alice measures in the basis $\\{|0\\rangle_A, |1\\rangle_A\\}$ and Bob measures in the basis $\\{|0\\rangle_B,|1\\rangle_B\\}$ as given above?\n",
    "\n",
    "Clearly we expect the overall measurement to have now 4 outcomes, 0 or 1 for Alice, as well as 0 and 1 for Bob. This is indeed the case, and we can compute the outcome probabilities by taking the basis for Alice and the one for Bob, and constructing the basis for both qubits together.\n",
    "\n",
    "This can be done using the tensor product. Find the <b> measurement basis for A and B</b>:\n",
    "\n",
    "1. $|0\\rangle_A \\otimes |0\\rangle_B$\n",
    "2. $|0\\rangle_A \\otimes |1\\rangle_B$\n",
    "3. $|1\\rangle_A \\otimes |0\\rangle_B$\n",
    "4. $|1\\rangle_A \\otimes |1\\rangle_B$\n",
    "\n",
    "For clarity we have filled in the first coefficient for the first listed tensor product:\n",
    "\n",
    "1. $|0\\rangle_A \\otimes |0\\rangle_B = \\begin{pmatrix} cos(\\frac{\\pi}{8}) \\\\ ? \\\\ ? \\\\ ? \\end{pmatrix}$\n",
    "\n",
    "Find such exact vector representations for the tensor products (1.), (2.), (3.) and (4.)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To help you out a little, use the Julia snippet below!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "combined basis (1.): [0.924,0.383,0.0,0.0]^T \n",
      "\n",
      "combined basis (2.): 3.0^T \n",
      "\n",
      "combined basis (3.): 3.0^T \n",
      "\n",
      "combined basis (4.): 3.0^T \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Let's first define Alice's basis. She measures in the standard basis\n",
    "alice0 = [1 ; 0];\n",
    "alice1 = [0 ; 1];\n",
    "\n",
    "# Let's now define Bob's basis.\n",
    "bob0 = [cos(pi/8); sin(pi/8)];\n",
    "bob1 = [- sin(pi/8); cos(pi/8)];\n",
    "\n",
    "# Compute the combined basis - your code goes here!\n",
    "cb_1 = kron(alice0,bob0)\n",
    "cb_2 = \n",
    "cb_3 = \n",
    "cb_4 = \n",
    "\n",
    "# To print, let's round \n",
    "digits = 3;\n",
    "cb_1 = round(cb_1,digits);\n",
    "cb_2 = round(cb_2,digits);\n",
    "cb_3 = round(cb_3,digits);\n",
    "cb_4 = round(cb_4,digits);\n",
    "\n",
    "println(\"combined basis (1.): $cb_1^T \\n\")\n",
    "println(\"combined basis (2.): $cb_2^T \\n\")\n",
    "println(\"combined basis (3.): $cb_3^T \\n\")\n",
    "println(\"combined basis (4.): $cb_4^T \\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\"> edX Exercise 6 </h3>\n",
    "\n",
    "Suppose now that Alice and Bob measure in the basis we constructed above. And let's suppose they measure the EPR pair. What are the probabilities of Alice getting outcome $x\\in \\{0,1\\}$ and Bob outcome $y \\in \\{0,1\\}$.\n",
    "\n",
    "$$ | \\Phi \\rangle = \\frac{ |0\\rangle_z \\otimes |0\\rangle_z + |1\\rangle_z \\otimes |1\\rangle_z }{\\sqrt{2}} = \\frac{1}{\\sqrt{2}}\\begin{pmatrix} 1 \\\\ 0 \\\\ 0 \\\\ 1\\end{pmatrix}\\:.$$\n",
    "\n",
    "What are the associated measurement probabilities rounded to 3 digits?\n",
    "\n",
    "1. $ p_{00} = \\Big|\\big( \\langle 0|_A \\otimes \\langle 0 |_B \\big) \\cdot | \\Phi \\rangle \\Big|^2$\n",
    "2. $ p_{01} = \\Big|\\big( \\langle 0|_A \\otimes \\langle 1 |_B \\big) \\cdot | \\Phi \\rangle \\Big|^2$\n",
    "3. $ p_{10} = \\Big|\\big( \\langle 1|_A \\otimes \\langle 0 |_B \\big) \\cdot | \\Phi \\rangle \\Big|^2$\n",
    "4. $ p_{11} = \\Big|\\big( \\langle 1|_A \\otimes \\langle 1 |_B \\big) \\cdot | \\Phi \\rangle \\Big|^2$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p_00: [0.427] \n",
      "\n",
      "p_01: [4.5 0.0 0.0 4.5] \n",
      "\n",
      "p_10: [4.5 0.0 0.0 4.5] \n",
      "\n",
      "p_11: [4.5 0.0 0.0 4.5] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "## in case you have succesfully ran the previous code block\n",
    "## go ahead and run this code block\n",
    "\n",
    "Phi = [1;0;0;1]/sqrt(2);\n",
    "\n",
    "# The probabilities follow from the squared inner product\n",
    "# betweeh Phi and the measurement basis \n",
    "p_00 = (Phi'*cb_1).^2\n",
    "p_01 = (Phi'*cb_2).^2\n",
    "p_10 = (Phi'*cb_3).^2\n",
    "p_11 = (Phi'*cb_4).^2\n",
    "\n",
    "# We will round the probabilities to 3 digits\n",
    "digits = 3;\n",
    "\n",
    "p_00 = round(p_00,digits)\n",
    "p_01 = round(p_01,digits)\n",
    "p_10 = round(p_10,digits)\n",
    "p_11 = round(p_11,digits)\n",
    "\n",
    "println(\"p_00: $p_00 \\n\")\n",
    "println(\"p_01: $p_01 \\n\")\n",
    "println(\"p_10: $p_10 \\n\")\n",
    "println(\"p_11: $p_11 \\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----\n",
    "<a id=\"transformations\"></a>\n",
    "<h2 style=\"color:#00A6D6;\">Unitary Transformations</h2>\n",
    "\n",
    "You have learned in class that transformations on qubits, are given by unitary transformations. Let's investigate such transformations in detail. \n",
    "\n",
    "As a warmup let's just define a matrix - the Hadamard transform, and verify that its indeed a unitary\n",
    "\n",
    "$$H = \\frac{1}{\\sqrt{2}}\\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2x2 Array{Float64,2}:\n",
       " 0.707107   0.707107\n",
       " 0.707107  -0.707107"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define the Hadamard transform as a matrix in Julia\n",
    "tH = [1 1;1 -1]/sqrt(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2x2 Array{Float64,2}:\n",
       " 1.0  0.0\n",
       " 0.0  1.0"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's now check whether the transformation is unitary by computing U' * U\n",
    "U = tH;\n",
    "U' * U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2x2 Array{Float64,2}:\n",
       " 1.0  0.0\n",
       " 0.0  1.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# And also U * U'\n",
    "U * U'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an exercise, you may wish to convince yourself that the Pauli matrices: X, Z and Y which we'll define below in Julia are also unitary!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: UndefVarError: X not defined\nwhile loading In[31], in expression starting on line 8",
     "output_type": "error",
     "traceback": [
      "LoadError: UndefVarError: X not defined\nwhile loading In[31], in expression starting on line 8",
      ""
     ]
    }
   ],
   "source": [
    "# Pauli X\n",
    "pX = [0 1;1 0];\n",
    "\n",
    "# Pauli Z\n",
    "pZ = [1 0;0 -1];\n",
    "\n",
    "# Pauli Y\n",
    "pY = im * X * Z;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us vizualize the effect of a unitary transformation $U$ on $\\lvert \\psi \\rangle$. What does $U|\\psi\\rangle$ look like?\n",
    "\n",
    "$$\\lvert \\psi(\\theta) \\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix} = \\begin{pmatrix} \\cos\\theta \\\\ \\sin{\\theta} \\end{pmatrix} $$\n",
    "\n",
    "\n",
    "<b> Click in the code block below and press shift+enter.</b>\n",
    "\n",
    "You will see a slider appear which lets you pick $\\theta$.\n",
    "\n",
    "The state vector $\\lvert \\psi(\\theta) \\rangle$ is plotted accordingly.\n",
    "\n",
    "Click the check-box to apply the unitary transformation (by default the Hadmard transformation) to $\\lvert \\psi(\\theta) \\rangle$ and you will see the resulting state vector $U \\lvert \\psi(\\theta) \\rangle$ plotted aswell.\n",
    "\n",
    "Vary $\\theta$ to see how $U \\lvert \\psi(\\theta) \\rangle$ and $\\lvert \\psi(\\theta) \\rangle$ change accordingly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Slider{Int64}(Signal{Int64}(0, nactions=0),\"θ\",0,-180:15:180,true)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x00000000205D1EF0>)"
      ]
     },
     "execution_count": 32,
     "metadata": {
      "comm_id": "07b9eef7-9e64-4a95-980e-3d30ed29a8ad",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unitary_transform_plot(tH) # we have entered tH as a default. You could also input X or Z transforms. \n",
    "                           # Note, complex valued state vectors are not supported"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\">edX Exercise 7</h3>\n",
    "\n",
    "Let's imagine that Alice wants to send a bit $x \\in \\{0,1\\}$ to Bob. Having gone all quantum, however, Alice has lost all means for classical communication. Unfortunately, Alice and Bob also have quite funny quantum devices.\n",
    "\n",
    "Concretely, Alice has a device that can only prepare the state $|+\\rangle$. Thankfully, however, she can apply one of two unitaries $U_0$ and $U_1$ of her choosing transforming her state to $|\\psi_x\\rangle = U_x |+\\rangle$. To be fair, we at least allow Alice some control over her circuit so that Alice can decide to $U_x$ corresponding to her input bit $x\\in\\{0,1\\}$. \n",
    "\n",
    "<img src=\"source/figure_exercise_7.svg\">\n",
    "\n",
    "Alice can now send her state $|\\psi_x \\rangle$ to Bob. Bob can only measure in the standard basis, and will take his measurement outcome $b \\in \\{0,1\\}$ to be the value of $x$. \n",
    "\n",
    "Your goal in this exercise is to come up with a protocol so that Alice can communicate $x$ to Bob, no matter whether $x=0$ or $x=1$. Concretely, your goal is to determine what transformations $U_0$ and $U_1$ she applies for the cases $x=0$, and $x=1$. \n",
    "\n",
    "In other words we ask you to find two unitaries $ U_0$ and $U_1$ that Alice can apply such that the probability that Bob obtains measurement outcome $B=x$ is given by\n",
    "\n",
    "$$ P(B=x) = \\big| \\langle x \\: \\lvert \\: U_x \\: \\rvert \\: + \\rangle \\big|^2 = 1 $$\n",
    "\n",
    "---\n",
    "\n",
    "You can check if you have found two such unitaries by making use of the code block just below.\n",
    "\n",
    "Enter $U_0$ and $U_1$ as is described and you will see the associated $p_0$ and $p_1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "You entered U_0 =\n",
      "[1 0\n",
      " 0 1]\n",
      "For this case the probability of Bob's measurement outcomes are:\n",
      "p_0 = 0.5\n",
      "p_1 = 0.5\n",
      "\n",
      "\n",
      " You entered U_1 =\n",
      "[1 0\n",
      " 0 1]\n",
      "For this case the probability of Bob's measurement outcomes are:\n",
      "p_0 = 0.5\n",
      "p_1 = 0.5\n"
     ]
    }
   ],
   "source": [
    "## enter values for U_0 - we'll start with the identity matrix\n",
    "U_0 = [1 0;0 1];\n",
    "\n",
    "## enter the second unitary U_0 - we'll start with the identity matrix\n",
    "U_1 = [1 0;0 1];\n",
    "\n",
    "# Let's define the standard basis and the plus state\n",
    "v0 = [1; 0];\n",
    "v1 = [0; 1];\n",
    "plus = [1; 1]/sqrt(2);\n",
    "\n",
    "## let's compute the outcome probabilities if Alice applies U_0\n",
    "\n",
    "# first, let's compute the output vector by applying the unitary transformation\n",
    "outVec = U_0 * plus;\n",
    "\n",
    "# then the probability that Bob measures b=0 is given by the inner product\n",
    "val = v0'*outVec;    \n",
    "p_0 = abs(val[1])^2; # take the square of the absolute value.\n",
    "\n",
    "val = v1'*outVec;\n",
    "p_1 = abs(val[1])^2;\n",
    "\n",
    "# for printing, let's round the outcomes\n",
    "digits = 3;\n",
    "p_0 = round(p_0, digits);\n",
    "p_1 = round(p_1,digits);\n",
    "\n",
    "println(\"You entered U_0 =\")\n",
    "println(U_0)\n",
    "println(\"For this case the probability of Bob's measurement outcomes are:\")\n",
    "println(\"p_0 = $p_0\")\n",
    "println(\"p_1 = $p_1\")\n",
    "\n",
    "## let's compute the outcome probabilities if Alice applies U_1\n",
    "\n",
    "# first, let's compute the output vector\n",
    "outVec = U_1 * plus;\n",
    "\n",
    "# then the probability that Bob measures b=0\n",
    "val = v0'*outVec;\n",
    "p_0 = abs(val[1])^2;\n",
    "\n",
    "val = v1'*outVec;\n",
    "p_1 = abs(val[1])^2;\n",
    "\n",
    "# for printing, let's round the outcomes\n",
    "digits = 3;\n",
    "p_0 = round(p_0, digits);\n",
    "p_1 = round(p_1,digits);\n",
    "\n",
    "println(\"\\n\\n You entered U_1 =\")\n",
    "println(U_0)\n",
    "println(\"For this case the probability of Bob's measurement outcomes are:\")\n",
    "println(\"p_0 = $p_0\")\n",
    "println(\"p_1 = $p_1\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"bloch_sphere\"></a>\n",
    "<h2 style=\"color:#00A6D6;\">Bloch Sphere</h2>\n",
    "\n",
    "In class, we learned a different way to write down a qubit, namely in terms of the Bloch sphere. It is important to understand that this representation is fundamentally distinct than the 2 dimensional vectors we saw above. Instead, recall from the videos and the lecture notes that qubits are parameterized by angles $\\theta$ and $\\phi$ in the Bloch sphere representation. Be careful to note that we will use $\\theta/2$ here, since we will draw in a very different space in 3D than the one in the plots above.\n",
    "\n",
    "$$\\left| \\psi \\right\\rangle = cos \\frac{\\theta}{2} \\: \\left| 0 \\right\\rangle + e^{i \\cdot \\phi} sin \\frac{\\theta}{2} \\: \\left| 1 \\right\\rangle = \\begin{pmatrix} cos \\frac{\\theta}{2} \\\\ e^{i \\cdot \\phi} sin \\frac{\\theta}{2} \\end{pmatrix}$$\n",
    "\n",
    "Let us now see how the qubits Bloch sphere representation follows from $\\theta$ and $\\phi$. Explore where the state lies in terms of the angles in the animation below.\n",
    "\n",
    "<b> Click in the code bloch below and press shift+enter to run the animation. </b>\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x00000000221CB470>)"
      ]
     },
     "execution_count": 41,
     "metadata": {
      "comm_id": "6cb200e5-f645-42e5-9ba9-35a518949192",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# One can pick θ, ϕ using the sliders that appear when the code is run.\n",
    "\n",
    "f1 = figure(figsize=(8,8))        # make an empty figure\n",
    "\n",
    "@manipulate for view = [15,60,-30], θ in 0:30:180, ϕ in -180:30:180\n",
    "    b1 = Bloch()         # make an empty Bloch sphere\n",
    "    add_vector(b1,[θ,ϕ]) # add a vector, with \n",
    "    withfig(f1) do\n",
    "        render(b1,view) # render the bloch sphere (incl. the vector)\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is instructive to see what happens if we transform a vector on the Bloch sphere with a unitary. As an example let's consider the following state - you may want to adapt it to get more intuition!\n",
    "\n",
    "$$ \\lvert \\psi \\rangle = \\cos\\frac{\\pi}{8} \\cdot \\lvert 0 \\rangle + \\sin\\frac{\\pi}{8} \\cdot \\lvert 1 \\rangle $$\n",
    "\n",
    "$$= \\frac{ \\sqrt{2 + \\sqrt{2} }}{2} \\lvert 0 \\rangle + \\frac{ \\sqrt{2 - \\sqrt{2} }}{2}  \\vert 1 \\rangle $$\n",
    "\n",
    "We'll find the following images\n",
    "\n",
    "1. $ X \\cdot \\lvert \\psi \\rangle $\n",
    "2. $ Y \\cdot \\lvert \\psi \\rangle $\n",
    "3. $ Z \\cdot \\lvert \\psi \\rangle $\n",
    "4. $ H \\cdot \\lvert \\psi \\rangle $\n",
    "\n",
    "By running the code cell below you can see these state represented on the Bloch sphere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Options{:ToggleButtons,Int64}(Signal{Int64}(15, nactions=0),\"view\",15,\"15\",Interact.OptionDict(Any[\"15\",\"-30\",\"60\"],Dict{Any,Any}(\"15\"=>15,\"-30\"=>-30,\"60\"=>60)),Any[],Any[])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Options{:ToggleButtons,ASCIIString}(Signal{ASCIIString}(I, nactions=0),\"transform\",\"I\",\"I\",Interact.OptionDict(Any[\"I\",\"X\",\"Y\",\"Z\",\"H\"],Dict{Any,Any}(\"Y\"=>\"Y\",\"Z\"=>\"Z\",\"I\"=>\"I\",\"X\"=>\"X\",\"H\"=>\"H\")),Any[],Any[])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000025F572E8>)"
      ]
     },
     "execution_count": 43,
     "metadata": {
      "comm_id": "f634ec95-d9f2-4c70-ae37-97277c78b48c",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "α = 0.5*sqrt(2 + sqrt(2)) # the parameters α and β associated with the vector above - change at will\n",
    "β = 0.5*sqrt(2 - sqrt(2))\n",
    "ket = [α; β];             # the associated vector\n",
    "\n",
    "# let us define the transforms\n",
    "pX = [0 1; 1 0]\n",
    "pY = [0 -im; im 0]\n",
    "pZ = [1 0; 0 -1]\n",
    "tH = [1 1; 1 -1]/sqrt(2)\n",
    "\n",
    "# we apply the I,X,Y,Z and H transvorm and find the corresponding Bloch vector using the function ket_to_bloch()\n",
    "v0 = ket_to_bloch(ket)      \n",
    "v1 = ket_to_bloch(pX*ket)    \n",
    "v2 = ket_to_bloch(pY*ket)    \n",
    "v3 = ket_to_bloch(pZ*ket)    \n",
    "v4 = ket_to_bloch(tH*ket)    \n",
    "\n",
    "# let us define a \"dictionary\": \"I\" belongs to v0, \"X\" belongs to v1, etc.\n",
    "vDict = Dict(   \"I\" => v0, \n",
    "                \"X\" => v1, \n",
    "                \"Y\" => v2, \n",
    "                \"Z\" => v3, \n",
    "                \"H\" => v4) \n",
    "\n",
    "# Now vDict[\"X\"] returns the vector v1.\n",
    "#     vDict[\"H\"] returns the vector v4.\n",
    "\n",
    "# let us create a new figure\n",
    "f9 = figure(figsize=(8,8)) \n",
    "\n",
    "# let us manipulate the view angle and the applied transform\n",
    "@manipulate for view in [15,-30,60], transform in [\"I\",\"X\",\"Y\",\"Z\",\"H\"]\n",
    "    \n",
    "    withfig(f9) do\n",
    "        b9 = Bloch()                 # make an empty Bloch sphere\n",
    "        add_vector(b9,v0)            # add the pre-transform Bloch vector\n",
    "        add_vector(b9,vDict[transform])    # add a transformed Bloch vector, \n",
    "                                           # note: vDict[] returns the vector associated with the transform \n",
    "        render(b9,view)      #  plot the Bloch Sphere\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\">edX Exercise 7 </h3>\n",
    "\n",
    "To become more familiar with the Bloch sphere we ask you to <b> find angles $\\theta$ and $\\phi$ </b> (in radians) with \n",
    "\n",
    "$$ | \\psi \\rangle = cos \\frac{\\theta}{2} \\: | 0 \\rangle + e^{i \\cdot \\phi} sin \\frac{\\theta}{2} \\: | 1 \\rangle = \\begin{pmatrix} cos \\frac{\\theta}{2} \\\\ e^{i \\cdot \\phi} sin \\frac{\\theta}{2} \\end{pmatrix}$$\n",
    "\n",
    "for the following states\n",
    "\n",
    "1. $|\\psi \\rangle = |+\\rangle$\n",
    "2. $|\\psi \\rangle = \\frac{\\sqrt{3}}{2}|0\\rangle + \\frac{i}{2} \\cdot |1\\rangle $\n",
    "\n",
    "<b style=\"color:#00A6D6;\"> Example </b>\n",
    "\n",
    "To help you get started let us give one example. Let us find $\\theta$ and $\\phi$ associated with\n",
    "\n",
    "$$|\\psi \\rangle = |0\\rangle\\: :$$\n",
    "\n",
    "We are looking for $\\theta$, $\\phi$ such that\n",
    "\n",
    "$$|0\\rangle = cos \\frac{\\theta}{2} \\: | 0 \\rangle + e^{i \\cdot \\phi} sin \\frac{\\theta}{2} \\: | 1 \\rangle $$\n",
    "\n",
    "Thus $$\\alpha = cos \\frac{\\theta}{2} = 1 $$ and $$\\beta = e^{i \\cdot \\phi} sin \\frac{\\theta}{2} = 0 \\:.$$ We find as a solution $\\theta = 0$ ( or $\\theta = 2\\pi$ )."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4 style=\"color:#00A6D6;\"> Supplement to Exercise 7</h4>\n",
    "\n",
    "<b> The code below can be used to vizualize the state on the Bloch sphere. Simply enter values for $\\theta$ and $\\phi$.</b> \n",
    "\n",
    "To plot a state on the Bloch sphere we should determine the associated Bloch vector $v$ (a cartesian vector):\n",
    "\n",
    "$$v = \\begin{pmatrix} v_x \\\\ v_y \\\\ v_z \\end{pmatrix} \\:.$$\n",
    " \n",
    "It turns out that $\\theta$ and $\\phi$ ---as introduced just now--- are the polar coordinates coordinates associated with $v$. For the radial coordinate $r$ it turns out that $r=1$. This follows from $\\langle \\psi | \\psi \\rangle = 1$.\n",
    "\n",
    "Translating to cartesian coordinates we recover\n",
    "\n",
    "$$ v = \\begin{pmatrix} \\sin\\theta \\cdot cos\\phi \\\\ \\sin\\theta \\cdot sin\\phi \\\\ \\cos\\theta \\end{pmatrix} $$ \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Options{:ToggleButtons,Int64}(Signal{Int64}(15, nactions=0),\"view\",15,\"15\",Interact.OptionDict(Any[\"15\",\"-30\",\"60\"],Dict{Any,Any}(\"15\"=>15,\"-30\"=>-30,\"60\"=>60)),Any[],Any[])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000001C8C8320>)"
      ]
     },
     "execution_count": 44,
     "metadata": {
      "comm_id": "33b500e9-1cb7-4eb3-aef0-399d166491d5",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = 45 # in degrees, change to your liking\n",
    "phi = 0    # in degrees\n",
    "\n",
    "# Side note: In the Julia language, sind(angle) takes as input an angle in degrees.\n",
    "#                                   sin(angle) takes as input an angle in radians.\n",
    "\n",
    "# Here we use degrees and thus sind, cosd\n",
    "\n",
    "bloch_vector = [sind(theta)*cosd(phi); sind(theta)*sind(phi); cosd(theta)]\n",
    "\n",
    "# the above can be altered to your liking, \n",
    "# define θ, ϕ either in terms of degrees or in terms of radians \n",
    "f8 = figure(figsize=(8,8))\n",
    "\n",
    "@manipulate for view in [15,-30,60]\n",
    "    withfig(f8) do\n",
    "        b8 = Bloch()                 # make an empty Bloch sphere\n",
    "        add_element(b8,bloch_vector) # add the vector to be plotted to the sphere\n",
    "        render(b8,view)              #  plot the Bloch Sphere\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-nc/4.0/88x31.png\" /></a><br /><span xmlns:dct=\"http://purl.org/dc/terms/\" property=\"dct:title\">Week 0 Exercises for QuCryptoX</span> by <a xmlns:cc=\"http://creativecommons.org/ns#\" href=\"http://qutech.nl/edu/\" property=\"cc:attributionName\" rel=\"cc:attributionURL\">QuTech Academy</a> is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc/4.0/\">Creative Commons Attribution-NonCommercial 4.0 International License</a>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.4.6",
   "language": "julia",
   "name": "julia-0.4"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.4.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}